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myininaya

  • 3 years ago

I have the following information: \[n=p^2q\] \[k \ge 4\] \[0<v<n\] \[0 \le x < pq\] \[y=\lceil \frac{(v-x^k) \mod n}{pq} \rceil \cdot (kx^{k-1})^{-1} \mod p\] I want to show: \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k-1}(ypq)^i \equiv x^k+kypqx^{k-1}\] the congruence is mod n

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  1. satellite73
    • 3 years ago
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    i can't even read this what class?

  2. myininaya
    • 3 years ago
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    i made a mistake \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k-i}(ypq)^i \equiv x^k+kypqx^{k-1}\] I'm trying to follow a proof but i don't know how they got from that one part to the other part

  3. satellite73
    • 3 years ago
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    yeah well i cannot read what it says. good luck

  4. myininaya
    • 3 years ago
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    http://www.cacr.math.uwaterloo.ca/hac/ its in chapter 11 on page 473 at the bottom

  5. myininaya
    • 3 years ago
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    ;p;

  6. myininaya
    • 3 years ago
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    lol*

  7. myininaya
    • 3 years ago
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    i wonder if james or zarkon could do it

  8. myininaya
    • 3 years ago
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    oh its zarkon lol

  9. satellite73
    • 3 years ago
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    good luck!

  10. KingGeorge
    • 3 years ago
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    ask me next semester when I've taken cryptography, and I might be able to help you, but right now, I haven't got a clue.

  11. Zarkon
    • 3 years ago
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    only the first two values of i will matter (i=0,1) for i>1 you have a \((pq)^2\) part which is \(p^2qq=nq\) which is zero nod n

  12. myininaya
    • 3 years ago
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    i don't see this (pq)^2 part

  13. myininaya
    • 3 years ago
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    george what kind of math have you had?

  14. Zarkon
    • 3 years ago
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    \[{k\choose i}x^{k-1}(ypq)^i\] for \(i\ge2\) \[{k\choose i}x^{k-1}(ypq)^i={k\choose i}x^{k-1}(y^i)(pq)^{i-2}p^2qq\] \[=\left({k\choose i}x^{k-1}(y^i)(pq)^{i-2}q\right)\times n\]

  15. myininaya
    • 3 years ago
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    ok i see

  16. myininaya
    • 3 years ago
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    you are so smart to notice the first two values will only matter since n mod n is like totally 0 thanks zarkon

  17. KingGeorge
    • 3 years ago
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    I've only had a year and a half of college level math so far, so that means, calc 1-3, lin. algebra, abstract algebra, and analysis

  18. Zarkon
    • 3 years ago
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    no problem :)

  19. myininaya
    • 3 years ago
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    is there any number theory in abstract algebra i can't remember

  20. KingGeorge
    • 3 years ago
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    not very much. I'm taking intro to number theory, and cryptography next semester.

  21. myininaya
    • 3 years ago
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    i like cryptography

  22. myininaya
    • 3 years ago
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    number theory is so cool and interesting to me although my skills suck right now

  23. KingGeorge
    • 3 years ago
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    It certainly sounds fun. I'm definitely enjoying my abstract algebra class right now. We had the barest hints of some number theory in discrete math so I'm not completely helpless.

  24. myininaya
    • 3 years ago
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    i like these math puzzles

  25. myininaya
    • 3 years ago
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    differential equations is not as fun to me but i do like the remedial kind lol

  26. myininaya
    • 3 years ago
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    zarkon do you think there is hope for my brain?

  27. KingGeorge
    • 3 years ago
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    From my experience, I don't like differential equations very much. Granted, I've never had a full course in it, but it just isn't my thing.

  28. Zarkon
    • 3 years ago
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    there is!

  29. myininaya
    • 3 years ago
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    i feel like i'm trapped inside with an apes' brain

  30. Zarkon
    • 3 years ago
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    A very smart ape ;)

  31. myininaya
    • 3 years ago
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    thanks i take that as a compliment

  32. Zarkon
    • 3 years ago
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    If you want a fun class...Take a course in measure theoretic probability theory.

  33. myininaya
    • 3 years ago
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    he says that because he is a stat nerd

  34. KingGeorge
    • 3 years ago
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    I don't think my school has that class...

  35. myininaya
    • 3 years ago
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    my doesn't either

  36. Zarkon
    • 3 years ago
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    or a class in stochastic processes

  37. Zarkon
    • 3 years ago
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    sometimes it will fall under the title of applied probability

  38. myininaya
    • 3 years ago
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    i think they might have that

  39. myininaya
    • 3 years ago
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    i always had a 10 foot pole when it came to statistics i only had to put it down when the course in stat was required

  40. KingGeorge
    • 3 years ago
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    I'm personally more of an algebra person. Stats was interesting at first, but then it got boring.

  41. myininaya
    • 3 years ago
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    There are some cool things though in stat i do admit

  42. Zarkon
    • 3 years ago
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    There is plenty of really nice mathematics in statistics

  43. KingGeorge
    • 3 years ago
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    It was the same with calculus for me. Interesting at first, and then it just stopped interesting me.

  44. Zarkon
    • 3 years ago
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    A lot of multivariate calculus and matrix theory

  45. myininaya
    • 3 years ago
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    zarkon can i ask another question

  46. myininaya
    • 3 years ago
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    this is my last problem with this proof...

  47. Zarkon
    • 3 years ago
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    ok

  48. myininaya
    • 3 years ago
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    omg never i got it lol

  49. myininaya
    • 3 years ago
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    i mean nvm

  50. myininaya
    • 3 years ago
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    i was typing it all out then i realized oh yeah lol

  51. Zarkon
    • 3 years ago
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    ok :)

  52. myininaya
    • 3 years ago
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    ok i feel good about this proof thanks for all your help

  53. Zarkon
    • 3 years ago
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    good...no problem

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spraguer (Moderator)
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